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Sets — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSets1 Mark
MCQ
Let $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $\ce{A ∪ B}?$
  • A
    $3$
  • ✓
    $6$
  • C
    $9$
  • D
    $18$
✓

Answer

Correct option: B.
$6$
$\ce{n(A ∪ B) = n(A) + n(B) − n(A ∩ B)}$
Now $A$ has $3$ elements and $B$ has $6 $elements.
If they are disjoint, then $\ce{n(A ∩ B)} = 0.$
$\therefore \ce{n(A ∪ B)} = 6 + 3 = 9$
If $\ce{A ⊂ B}$ then $\ce{A ∪ B = B}$
$\therefore (A ∪ B) = n(B) = 6$
$B$ cannot be a subset of $A$ and hence the other possibility of $\ce{A ∪ B = A}$ is ruled out.

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